Ind. Eng. Chem. Res., Vol. 27, No. 8, 1988 1511 equilibria. The same type of information for a liquid system can, in principle, be derived from liquid chromatographic (LC) measurements, but the potential of this approach does not appear to have been exploited to any extent. In contrast to gas chromatography, liquid chromatography always involves counterdiffusion of sorbate and solvent molecules within the zeolite micropores. Indeed, when the molar volumes of sorbate and solvent are similar, the exchange process must involve equimolar counterdiffusion. There has been much debate as to whether or not the diffusivities measured under transport conditions in a conventional vapor-phase sorption or chromatographic experiment are really representative of the diffusivities under counterdiffusion conditions, as in a catalytic reaction. Liquid chromatography offers, in principle, a simple way of measuring diffusivities under counterdiffusion conditions, and if the solvent is changed, the effect of the counterdiffusing species can be easily investigated. The method also has the advantage that measurements may be easily confined to the linear region of the equilibrium isotherm, making the results easier to interpret theoretically. By contrast, in a conventional batch sorption experiment, the progress of the exchange is followed by monitoring the liquid-phase concentration so a relatively large concentration change is required to ensure accurate results. Under these conditions, it may be difficult to confine the experiment to the linear region. The objectives of the present study were (i) to explore the potential of LC as a means of measuring intracrystalline diffusion, (ii) to investigate the diffusion of some representative sorbates in NaX crystals a t high loading, and (iii) to investigate the effect of the counterdiffusing species and to provide a basis for comparison with vapor-phase sorption data. Experimental Method The chromatographic method depends on measuring the concentration response of a small packed column in a flow system when a pulse of an adsorbable component is introduced at the inlet. The mean retention time (or retention volume) measures the holdup in the column, from which the adsorption equilibrium constant may be calculated, while the broadening of the response peak measures the combined effects of axial dispersion and mass-transfer resistance. To permit a simple interpretation of the results, the measurements must be confined to the linear region of the equilibrium isotherm and any extra column dead volume, which introduces additional time delays and/or dispersion should be minimized. If the objective is to measure intracrystalline diffusion, then the experimental conditions should be chosen to maximize this contribution and to minimize contributions to the broadening of the response peak from axial dispersion and extracrystalline mass-transfer resistance. These general requirements apply equally to both gas and liquid systems, but because of the higher molecular density, the impact of dead volume tends to be much more severe in liquid chromatography. Furthermore, the limitations imposed by the linearity requirement coupled with limited sensitivity of the common LC detectors also appear to be more restrictive for liquid systems. We sought to eliminate any macropore diffusion resistance and to maximize the contribution of intracrystalline resistance by packing the column with relatively large (20- and 40-bm diameter) unaggregated NaX zeolite crystals, rather than with the small (1-2 bm) crystals or pelleted material which is available commercially. The NaX crystals were synthesized by Charnell’s (1971) method
r 24”
or 9 m m
Nitex Screen Support
I
Ferrule VL” to 0.2” Valco Zero Dead Volume Fitting
f Valka Female Nut
Figure 1. Details of experimental column.
and fractionated into convenient size fractions by wet sieving through “Nitex” nylon screens. The mean crystal size was determined from scanning electron micrographs. The choice of sorbate and solvent was dictated largely by practical considerations. With an aromatic sorbate in a saturated hydrocarbon solvent, one may use an ultraviolet absorption detector which has the advantages of high sensitivity and low dead volume. We therefore used benzene and o-xylene as the sorbates with cyclohexane and n-hexane as solvents. A few experiments were also made in aqueous systems with phenol and acetone as the sorbates. Since, on NaX zeolite, the aromatics are adsorbed much more strongly than the saturated hydrocarbon solvents, retention volumes are large. Within the accessible range of flow rate, the retention time therefore becomes inconveniently long unless a very short column is used. On the other hand, if a short column is used, strict attention must be paid to the detailed design of the system since any dead volume or extra column dispersion will be proportionately more significant. Initial tests were made with several different column lengths before we eventually settled on the use of very short columns (0.9 and 2.4 cm) which gave retention times in the range 500-5000 s over the experimental range (flow rates 0.05-0.5 mL/min). Columns were constructed in the manner indicated in Figure 1. Small bore tubing (0.12-mm i.d.) and Valco “zero dead volume” fittings were used for the entire flow system between the injector and detector. The chromatograph was a standard Hewlett-Packard HP1090 fitted with an automatic sample injection system and either UV or refractive index detectors. In preliminary experiments, we quickly found that to obtain reproducible results it is essential to keep both the solvent and sorbate free from moisture; otherwise, even at ppm levels, the zeolite rapidly deactivates by picking up moisture, thus losing capacity. The problem was solved by adding activated molecular sieve to both solvent and sorbate and maintaining the solvent reservoir under a continuous purge of dry helium to prevent any contact with atmospheric air. In addition, a 10-cm X 0.4-cm column packed with dehydrated 5A sieves was included in the flow line from the solvent reservoir to injector. This column was removed periodically and reactivated by purging at 350 “C under a stream of helium. Analysis of Chromatograms. The kinetic and equilibrium parameters were extracted from the experimental chromatograms by the method of moments. For a linear chromatographic system in which the column is packed with unaggregated zeolite crystals, the first and second moments of the response to a perfect pulse injection are given by (see, for example, Ruthven (1984))
1512 Ind. Eng. Chem. Res., Vol. 27, No. 8, 1988 Table I. Details of Experimental Columns av crystal column length, cm i.d., cm diam., Wm
r m c tdt
J,
-.
1 2
dt L m c ( t- b ) 2 dt
0.9 2.4
0.44 0.44
103~,p,
L m cdt
H is the height equivalent to a theoretical plate (HETP). Provided that the sorbate is adsorbed much more strongly than the solvent (K >> l.O), the last term in eq 3 may be neglected to give the simplified expression
r , pm
T , "C
K
S-1
cm2.s-1
10
acetone-HzO
10
40 80 40
benzene-C6H12
10
10
16 35 26 51 0.8 1.2 1.67 3.4 4.7 5.4 8.2 18.5 1.05 2.2 5.0 0.5
16 35 26 51 0.8 1.2 1.67 3.4
benzene-C6H,,
1.12 0.98 1.05 1.05 113 91.4 60 48 99.5 80.5 56 34 307 178 102
benzene-C6H14 o-xylene-C&,,
Based on the correlation of Wilson and Geankoplis (1966), at low Reynolds numbers in a liquid system,
-
which, for the present experimental conditions, gives Sh 5-8. The influence of external film resistance will be negligible provided r/3kf > 2.0 KDC
-
(6)
-
For all systems studied this condition was easily fulfilled 100, D, 4.5 (e.g., for benzene-n-hexane at 40 "C, K X cm2-s-l (see, for example, Reid et al. (1977), Ghai and Dullien (197411, D, 4.7 X c m 2 d ,D,/KD, 100). Furthermore, the experimental results confirm the absence of significant external film resistance, as discussed below. However, it is also clear that the intrusion of external fluid film resistance imposes severe restrictions on the range of intracrystalline diffusivities accessible to measurement by this technique. It follows from eq 5 that kf a r-2/3. The internal and external mass-transfer terms therefore show almost the same dependence on crystal size (r5I3and ?). Increasing the crystal size therefore gives only a marginal increase in the relative importance of the intracrystalline resistance. The use of relatively large crystals is, however, necessary to ensure uniform column packing with acceptably low axial dispersion. In columns packed with small 1-2-km commercial crystals, the axial dispersion term tends to be completely dominant, and it is therefore not possible to measure the mass-transfer resistance with any confidence. Column Preparation and Preconditioning. Details of the experimental columns are given in Table I. The column was packed with the selected size fraction of NaX crystals and dehydrated a t elevated temperature under a helium purge (35 mL/min). The temperature was raised from ambient to 350 "C over a period of about 12 h and then maintained at 350 "C for a further 20 h in order to ensure complete dehydration. The column was then
-
-
109~,,
system phenol-H?O
80 40 50 60 75 .-
